I doubt there are any words meaningfully conserved across all languages. That sort of thing would be the holy grail of phylolinguistics and a lot of very smart people have spent good chunks of their lives turning up nothing of the sort.
Even in Eurasia, I think there are languages like Mongolian - "eej" is mother in Mongolian. But the general premise that these are the simplest words for babies is still possible : eej is mother, aav, father.
K'iche (Mayan): chuch, qajaw
Mam (Mayan): txu, man
Kaurna (Pama-Nyungan): ngangkita, yarlita
Gurindji (Pama-Nyungan): ngamayi, ngaji
I doubt there are any words meaningfully conserved across all languages. That sort of thing would be the holy grail of phylolinguistics and a lot of very smart people have spent good chunks of their lives turning up nothing of the sort.